Uncertainty quantification for multi-view learning is motivated by the increasing use of multi-view data in scientific problems. A common variant of multi-view learning is late fusion: train separate predictors on individual views and combine them after single-view predictions are available. Existing methods for uncertainty quantification for late fusion often rely on undesirable distributional assumptions for validity. Conformal prediction is one approach that avoids such distributional assumptions. However, naively applying conformal prediction to late-stage fusion pipelines often produces overly conservative and uninformative prediction regions, limiting its downstream utility. We propose a novel methodology, Multi-View Conformal Prediction (MVCP), where conformal prediction is instead performed separately on the single-view predictors and only fused subsequently. Our framework extends the standard scalar formulation of a score function to a multivariate score that produces more efficient downstream prediction regions in both classification and regression settings. We then demonstrate that such improvements can be realized in methods built atop conformalized regressors, specifically in robust predict-then-optimize pipelines.

翻译：多视图学习的不确定性量化受到科学问题中多视图数据日益广泛应用的推动。多视图学习的一个常见变体是后期融合：在单个视图上分别训练预测器，并在单视图预测可用后将其组合。现有的后期融合不确定性量化方法通常依赖于不理想的分布假设以保证有效性。保形预测是一种避免此类分布假设的方法。然而，将保形预测简单应用于后期融合流程通常会产生过于保守且信息量不足的预测区域，限制了其下游实用性。我们提出了一种新颖的方法论——多视图保形预测（MVCP），其中保形预测改为在单视图预测器上分别执行，仅在此后进行融合。我们的框架将评分函数的标准标量形式扩展为多元评分，从而在分类和回归设置中均能产生更高效的下游预测区域。随后我们证明，此类改进可在基于保形化回归器的方法中实现，特别是在鲁棒的预测后优化流程中。